Weighted Koppelman formulas and the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mover accent="true"><mml:mo>∂</mml:mo><mml:mo>¯</mml:mo></mml:mover></mml:math>-equation on an analytic space

Andersson, Mats; Samuelsson, Håkan

doi:10.1016/j.jfa.2011.02.018

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Cited by 13 publications

(2 citation statements)

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“…In this or a similar formulation this phenomenon has extensively been investigated in many situations, including Stein manifolds and spaces, (n − 1)-complete normal complex spaces and so on; see [2]- [6], [10], [11], [16], [20], [22], [26] and [27].…”

Section: § 1 Introductionmentioning

confidence: 99%

The Hartogs extension phenomenon in almost homogeneous algebraic varieties

Феклистов

2022

Sb. Math.

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Section: § 1 Introductionmentioning

confidence: 99%

The Hartogs extension phenomenon in almost homogeneous algebraic varieties

Феклистов

2022

Sb. Math.

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“…A natural question arises: is this true for general complex analytic spaces? This phenomenon has been extensively studied in many situations, including Stein manifolds and spaces, (n − 1)-complete normal complex spaces and so on (see, for instance, [18,1,3,19,28,30,31,26,11,25,33]).…”

Section: Introductionmentioning

confidence: 99%

The Hartogs Extension Phenomenon in Toric Varieties

Sergey

Shchuplev

2021

J Geom Anal

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$$L^2$$ L 2 -properties of the $$\overline{\partial }$$ ∂ ¯ and the $$\overline{\partial }$$ ∂ ¯ -Neumann operator on spaces with isolated singularities

Øvrelid

Ruppenthal

2014

Math. Ann.

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Let X be a Hermitian complex space of pure dimension with only isolated singularities and π : M → X a resolution of singularities. Let Ω ⊂⊂ X be a domain with no singularities in the boundary, Ω * = Ω \ Sing X and Ω ′ = π −1 (Ω). We relate L 2 -properties of the ∂ and the ∂-Neumann operator on Ω * to properties of the corresponding operators on Ω ′ (where the situation is classically well understood). Outside some middle degrees, there are compact solution operators for the ∂-equation on Ω * exactly if there are such operators on the resolution Ω ′ , and the ∂-Neumann operator is compact on Ω * exactly if it is compact on Ω ′ .

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Weighted Koppelman formulas and the ∂¯-equation on an analytic space

Abstract: Let X be an analytic space of pure dimension. We introduce a formalism to generate intrinsic weighted Koppelman formulas on X that provide solutions to the∂-equation. We obtain new existence results for thē ∂-equation, as well as new proofs of various known results.

Cited by 13 publications

References 22 publications

The Hartogs extension phenomenon in almost homogeneous algebraic varieties

The Hartogs extension phenomenon in almost homogeneous algebraic varieties

The Hartogs Extension Phenomenon in Toric Varieties

$$L^2$$ L 2 -properties of the $$\overline{\partial }$$ ∂ ¯ and the $$\overline{\partial }$$ ∂ ¯ -Neumann operator on spaces with isolated singularities

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